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Puzzler: The farmer and the 40 lb stone (10/22/11) (NO ANSWER GIVEN)

edited October 2011 in The Show
The Puzzle of Oct 22, 2011: A farmer has a 40 lb stone that he uses to measure out bales of hay on a 2 sided balance. He loans it to a friend who accidentally breaks it into 4 pieces. Instead of being angry, the farmer is quite happy. He says to the friend, "You managed to break it into just the right 4 pieces that will now let me weigh any weight between 1 and 40." What are the weights of the 4 pieces?

I propose a second challenge: Are there any posters out there with black belts in Google who can find the solution on the internet? The solution is out there.
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